To improve the light extraction efficiency (LEE) of GaN-LED with hemisphere microlens array surface structure, four kinds of waveguide materials such as GaN, ZnO, SiO2 and polystyrene are studied with finite-difference time-domain method. The simulation results are further tested by mode analysis method. The results show that the LEE can be improved when the refractive index grows higher, and the LEE of microlens array with bigger radius hemisphere is better in the subwavelength structure. The optimized model with 600 nm radius hemisphere microlens array of GaN material, with which the LEE exhibites 5.66 times enhancement than that of the planar LED, is the best output among those results. The above results are analyzed and verified by the asymmetric planar mode analysis method with equivalent refractive index. These results provide a theoretical guide on the practical design and optimization of highly efficient GaN-based LED.